Debt markets rallied on the appointment of the center-left's Letta, which ended two months of political impasse after Italy's inconclusive national election. Yields on the country's benchmark 10-year debt fell on the news and stood at 3.89 percent on Tuesday morning, despite a sell-off in Italian equities.

However, some strategists were concerned about the tone and content of Letta's maiden speech, which emphasized the need for growth rather than austerity, potentially putting him on a coalition course with Germany's Angela Merkel. He also halted an unpopular property tax and hinted he may delay an increase in sales tax, potentially undoing some of Mario Monti's reforms.

"His economic program has a distinctly 'Hollandiste' tone to it," Nicholas Spiro, head of Spiro Sovereign Strategy said in a research note.

"Letta has failed to articulate a credible economic agenda to extricate Italy from recession and deliver sustainable growth. The fact that he's giving himself only 18 months hardly inspires confidence."

"Without more meaningful reforms to the country's labor and product markets, including an overhaul of Italy's education system and a further liberalization of protected professions, Italy will continue to suffer from low growth and high unemployment," he said in a research note on Tuesday.

"We doubt that the current government will have the willingness, determination and parliamentary majorities to push through such long-overdue reforms, leaving the country's growth potential as weak as ever and its mounting debt burden arguably unsustainable."

Senior fixed income broker at Mint Partners, Bill Blain, said the question is now whether Italian and Spanish bonds are poised on a precipice, or ready to rally further.

"We are in new markets," he said in a morning note on Tuesday. "This may be the moment to get over your doubts and fears about the European project and put your Italian and Spanish buying boots back on. Lace 'em up tight."

The ongoing de-leveraging of the European banking system and the increasing domestication of the peripheral bond markets all hint at further gains for debt markets, he said.

Director of Research at IDEAglobal Mike Gallagher said there was increasing divergence between Italy's liquidity-driven assets and its economic fundamentals, and said his technical analysis suggests bond yields will spike later this year.

"What we're looking for is for a return to European-centric crisis… We feel we are stuck in recession, we have rising political and social tensions and we have got inconsistent crisis management," he told CNBC.com.